A Simple Model for Stretched Exponential Relaxation in Three‐Level Jumping Process

Abstract

In this study, operator formalism is briefly introduced which is used to model Debye‐type relaxation with three‐level jumping based on Markovian framework. The author generalizes this formalism to the non‐Markovian process to model the non‐exponential relaxation and internal friction of real bcc metals or systems like Snoek‐type. By using this formalism, stretched exponential relaxation and the frequency and temperature dependence of internal friction depending upon β parameter are obtained. For β = 1, it is shown that the relaxation is exponential which obeys Debye law, and the frequency and temperature dependence of internal peak are represented by a single Debye peak. However, for 0 < β < 1 the author shows that relaxation is given by stretched exponential form, and the internal friction deviates from single Debye peak. It is concluded that β represents the memory, aging, and coupling effects of stochastic dynamics in complex materials.

Molecular dynamics investigation of benzoic acid in confined spaces

“…It is difficult to attach a clear physical meaning to such figures, as testified by the rich and ongoing debate on the application of the KWW function to relaxation phenomena in liquids and glasses. 48,49,51–53 However, it is worth noting our β ⊥ estimates lie around β SR = 3/5 = 0.6, which is the value expected for relaxation dynamics slowed down by short-range forces in three-dimensional spaces. 48 Likely, this further points out the pivotal role of short hydrogen bonds in determining the dynamics of the liquid at the molecular scale.…”

How to Make the Stress Relaxation Experiment for Polymers More Informative

“…The Kohlrausch-Williams-Watts (KWW) relaxation function has been widely used to describe the relaxation behavior of glass-forming liquids and complex systems [47]. However, in the ongoing debate on the application of the KWW function to relaxation phenomena in different polymers [48,49], in particular to liquids and glasses, this model is widely used. Examples of research published this year alone include modeling of the mechanical properties of highly elastic and tough polymer binders with interweaving polyacrylic acid (PAA) with a poly(urea-urethane) (PUU) elastomer [50]; modeling of the relaxation curve describing the local dynamics of ions and hydration water near the RNA interface [51]; studying the relaxation processes for bulk antipsychotic API aripiprazole (APZ) and the active pharmaceutical ingredients (API) incorporating anodic aluminum oxide (AAO) or silica (SiO 2 ) systems that are collected during the "slow-heating" procedure [52]; description of the rheological properties of the cross-linked blends of Xanthan gum and polyvinylpyrrolidone-based solid polymer electrolyte [53]; studies concerning the stress relaxation process in annealed metallic and polymer glasses [54]; and the stress relaxation behavior of glass-fiber-reinforced thermoplastic composites [55].…”

The Analysis of WJ Distribution as an Extended Gaussian Function: Case Study

“…Showing the ubiquitous irreversibility characteristics on the atomic, molecular, or electronic scale and the dynamic nature of irreversible processes, the KWW relaxation function or the stretched exponential relaxation function is a phenomenal observation in complex systems from the intricate behavior of liquids and glasses, the folding of proteins to the structure and dynamics of atomic and molecular clusters and well delineating the phenomena of important time-dependent dynamic processes [13,22,23]. The research has a long history of continuous interest, research inputs, and technological importance, in condensed matter physics in particular, as manifested by the fact that our research outcomes [17] have prompted wide attention from diverse fields [23][24][25][26][27][28][29][30][31][32][33][34].…”